The present invention pertains to a Reed-Solomon encoding device and method and a Reed-Solomon decoding device and method for use as error correction codes of recording media and digital transmission.
Reed-Solomon codes (hereinafter referred to as RS codes) have high encoding efficiency and are very effective in eliminating burst errors. Consequently, they are mainly used as outside codes of recording media and digital transmission. Also, with advancements in IC technology, it has become possible to fabricate encoding/decoding ICs as single chips corresponding to codes with a relatively high correction power for 8-byte or higher correction. As a result, its application range has expanded rapidly.
RS codes are characterized by a very high degree of design flexibility pertaining to the forming method of encoding. For example, even for a Galois field GF(2m) that is frequently used in RS codes, usually, as a condition of its field formation polynomial, the period should be 2mxe2x88x921. Consequently, there exist various types. In addition, there is a wide range for selecting the roots of the code forming polynomial that realizes the same correction power. That is, if the root of the field formation polynomial is xcex1, then as a condition for realizing a correction of t bytes, the root of the code forming polynomial can be selected from a group of at least 2t consecutive powers of xcex1, that is, (xcex1b, xcex1b+1, xcex1b+2, . . . xcex1b+2txe2x88x921). Here, b may be any integer. Consequently, there exists a significant number of different RS codes for the same t-byte correction.
From the standpoint of system development, such design flexibility is desirable. However, from the standpoint of standardization, this is undesirable. The requirement for correction power, etc., usually dictates the need for a Galois field GF(28) with 28 elements. However, there are various other parameters. The code length and correction power, of course, depend on the specific requirements. Among the trivial differences, the greatest influence is the difference in the field formation polynomial. For example, if RS encoding/decoding devices are formed to correspond to two systems and the field formation polynomials are different, then the multipliers of their Galois fields will also be different. Consequently, compatibility is impossible. In particular, when efforts are made to correspond to that which has a higher correction power, the proportion of the multiplier of the aforementioned Galois field in the circuit scale becomes larger. In the prior art, one must prepare multipliers of Galois fields corresponding to the two systems. This leads to an increase in the cost of the device.
In practice, even in the same digital transmission field, the field formation polynomial used in satellite communications and those used in satellite broadcasting are different. This is mainly because standardization is difficult due to differences in jurisdiction between the communication field and the broadcasting field. Also, when the aforementioned standards were set up, there was little need for a common field formation polynomial.
In recent years, however, during discussions regarding the unification of communication and broadcasting, the aforementioned need became clearer. However, it is very hard to make changes to realize complete standardization. Also, for the RS codes adopted for recording media, manufacturers usually lead the development, and in few cases is the same field formation polynomial adopted for recording media developed by different manufacturers.
FIG. 11 is a schematic diagram illustrating a conventional RS encoding/decoding device handling two or more RS codes, that is, for handling RSa code, RSb code, . . . RSx code. It has multipliers (10a)-(10x) of Galois fields GFa(2m), GFb(2m), . . . GFx(2m) corresponding to field formation polynomials, respectively, and multiplication coefficient memory units (11a)-(11x) that store a collection of multiplication coefficients of Galois fields {xcex1a[l]}, {xcex2b[l]}, . . . {"khgr"x[k]}, corresponding to the code forming polynomials, respectively. The conventional RS encoding/decoding device also has inverse element arithmetic circuits 12a-12x corresponding to the codes for division.
In the following, in order to simplify the explanation, conventional RS encoding/decoding device 1 that handles two RS codes, that is, RSa code and RSb code will be used. Here, for both RSa code and RSb code, the correction power corresponds to a correction of t bytes.
FIG. 12 is a diagram illustrating surplus arithmetic circuit 202 that forms conventional RS encoding/decoding device 1. In surplus arithmetic circuit 202, collection of multiplication coefficients of Galois fields {xcex1ao[i]}, i=0-L is contained in said collection of multiplication coefficients of Galois fields {xcex1a[i]}, and collection of multiplication coefficients of Galois fields {xcex2be[j]}, j=0-L is contained in said collection of multiplication coefficients of Galois fields {xcex2b[j]}. Here, L is 2txe2x88x921 or 2t (same in the following).
As shown in FIG. 12, surplus arithmetic circuit 202 of the polynomial has multipliers 203-0xcx9c203-L, multipliers 208-0xcx9c208-L, switches 204-0xcx9c204-L, registers 205-0xcx9c205-L, adders 206-1xcx9c206-L, and adder 207.
Switches 204-0xcx9c204-L select multipliers 203-0xcx9c203-L in the case of RSa encoding and multipliers 208-0xcx9c208-L in the case of RSb encoding.
Usually, RS decoding device is composed of syndrome arithmetic circuit, error location polynomial and evaluation polynomial arithmetic circuit, error location detecting circuit, evaluation value detecting circuit, and correction execution circuit. Of those, for said error location polynomial arithmetic circuit and evaluation polynomial arithmetic circuit, the known methods include the Euclidean algorithm method and the Barlekamp-Massey method.
FIG. 13 is a diagram illustrating a conventional constitutional example of syndrome arithmetic circuit 209 corresponding to said two RS codes. Here, the collection of multiplication coefficients of Galois fields {xcex1as[i]}, i=0-L is contained in said {xcex1a[i]}, and the collection of multiplication coefficients of Galois fields {xcex2bs[j]}, j=0-L is contained in said {xcex2b[j]}.
As shown in FIG. 13, syndrome arithmetic circuit 209 has multipliers 213-0xcx9c213-L, switches 214-0xcx9c214-L, registers 215-0xcx9c215-L, adders 216-0xcx9c216-L, and multipliers 217-0xcx9c217-L.
Switches 214-0xcx9c214-L select multipliers 213-0xcx9c213-L in the case of RSa encoding and multipliers 217-0xcx9c217-L in the case of RSb encoding.
FIG. 14 is a diagram illustrating an example of the conventional constitution of polynomial division circuit 221, one of the major elements of the error location polynomial and evaluation polynomial arithmetic circuit, corresponding to said two RS codes.
As shown in FIG. 14, polynomial division circuit 221 has switches 222-0xcx9c222-L, multipliers 223-0xcx9c223-L, multipliers 228-0xcx9c228-L, registers 225-0xcx9c225-L, registers 224-0xcx9c224-L, adders 226-0xcx9c226-L, registers 227, 229, inverse element arithmetic circuits 231, 232, multipliers 230, 231, and switch 234.
Switches 222-0xcx9c222-L select multipliers 223-0xcx9c223-L in the case of RSa encoding and multipliers 228-0xcx9c228-L in the case of RSb encoding. Also, switch 234 selects multiplier 230 in the case of RSa encoding and multiplier 231 in the case of RSb encoding.
FIG. 15 is a diagram illustrating an example of the conventional constitution of polynomial multiplier 241, a major element of error location polynomial and evaluation polynomial arithmetic circuit, corresponding to said two RS codes.
As shown in FIG. 15, polynomial multiplier 241 has multipliers 243-0xcx9c243-L, multipliers 248-0xcx9c248-L, switches 242-0xcx9c242-L, registers 245-0xcx9c245-L, adders 246-1xcx9c246-L, and registers 247-0xcx9c247-L.
Switches 242-0xcx9c242-L select multipliers 243-0xcx9c243-L in the case of RSa encoding and multipliers 248-0xcx9c248-L in the case of RSb encoding.
FIG. 16 is a diagram illustrating an example of the conventional constitution of error location detecting circuit 251 corresponding to said two RS codes.
As shown in FIG. 16, error location detecting circuit 251 has multipliers 252-0xcx9c252-n, multipliers 258-0xcx9c258-n, switches 252-0xcx9c252-n, registers 255-0xcx9c255-n, adders 256-1xcx9c256-n0, and detecting circuit 257.
Switches 252-0xcx9c252-n select multipliers 252-0xcx9c252-n in the case of RSa encoding and multipliers 258-0xcx9c258-n in the case of RSb encoding.
Here, the collection of multiplication coefficients of Galois fields {xcex1ac[i]}, i=0xcx9cn=t is contained in said {xcex1a[i]}, and the collection of multiplication coefficients of Galois fields {xcex2bc[j]}, j=0xcx9cn=t is contained in said {xcex2b[j]}. When erasure-and-error correction is carried out, one has I=0xcx9cn=2t, j=0xcx9cn=2t.
FIG. 17 is a diagram illustrating an example of the conventional constitution of evaluation value detecting circuit 261 corresponding to said two RS codes.
As shown in FIG. 17, evaluation value detecting circuit 261 has multipliers 262-0xcx9c262-(nxe2x88x921), multipliers 267-0xcx9c267-(nxe2x88x921), switches 262-0xcx9c262-(nxe2x88x921), registers 265-0xcx9c265-(nxe2x88x921), and adders 266-1xcx9c266-(nxe2x88x921).
Switches 262-0xcx9c262-(nxe2x88x921) select multipliers 262-0xcx9c262-(nxe2x88x921) in the case of RSa encoding and multipliers 267-0xcx9c267-(nxe2x88x921) in the case of RSb encoding.
Here, the collection of multiplication coefficients of Galois fields {xcex1av[i]}, i=0xcx9cnxe2x88x921 is contained in said {xcex1a[i]}, and the collection of multiplication coefficients of Galois fields {xcex2bv[j]}, j=0xcx9cnxe2x88x921 is contained in said {xcex2b[j]}.
In this way, in the conventional constitution of RS encoding/decoding device for handling two or more RS codes, it is necessary to have multipliers and inverse element arithmetic circuits corresponding to the respective field formation polynomials, and to be able to switch between them.
Also, in the aforementioned constitution, when changes takes place in the Galois field of the encoding target data and decoding target data, it is necessary to change the hardware constitution. As a result, it is impossible to handle diverse types of Galois field data encoding/decoding in a flexible way, which is undesirable.
The purpose of the present invention is to solve the aforementioned problems of the conventional methods by providing a Reed-Solomon encoding device and method that can reduce the scale of the device and can decrease the cost of the device.
Another purpose of the present invention is to provide a Reed-Solomon encoding device and method that can perform diversified Galois field data encoding in a flexible way.
Yet another purpose of the present invention is to provide a Reed-Solomon decoding method and device that can reduce the scale and cost of the device.
Yet another purpose of the present invention is to provide a Reed-Solomon decoding device and method that can perform diversified Galois field data decoding in a flexible way.
In order to solve the aforementioned problems and to realize the aforementioned purposes, the present invention provides a type of Reed-Solomon encoding device characterized by the fact that the Reed-Solomon encoding device that handles multiple RS (Reed-Solomon) codes by means of different field formation polynomials has the following means: a first Galois field transformation means that transforms the input encoding target data into data of a prescribed Galois field on the basis of the input first Galois field transformation parameter, an encoding means that performs encoding processing by means of said transformed Galois field for said transformed encoding target data, a second Galois field transformation means that inverse transforms said encoded data into data of said Galois field before transformation on the basis of input second Galois field transformation parameter, and a parameter output means that outputs said first Galois field transformation parameter and said second Galois field transformation parameter.
In the Reed-Solomon encoding device of the present invention, a first Galois field transformation means and a second Galois field transformation means are used. For any of multiple RS codes, encoding processing is performed using a prescribed Galois field in the encoding means. As a result, there is no need to use multiplier and inverse element arithmetic units to correspond to each of multiple RS codes separately in the encoding means, so that the circuit scale can be reduced significantly.
Also, because said first Galois field transformation means and second Galois field transformation means perform Galois field transformation on the basis of the first Galois field transformation parameter and second Galois field transformation parameter output from the parameter output means, respectively, it is possible to make diversified and flexible changes for the contents of the Galois field transformation.
For the Reed-Solomon encoding device of the present invention, it is preferred that said encoding means have a multiplier corresponding to said transformed Galois field.
Also, the Reed-Solomon encoding device of the present invention preferably has the following features: said multiple RS codes are RSa codes and RSb codes using different field formation polynomials; the encoding symbols are Galois fields GFa(2m) and GFb(2m) extended on the basis of different mth field formation polynomials Gpa(x) and Gpb(x) on Galois field GF(2), respectively; for xcex1, which is a root of said Gpa(x) and a primitive element of said GFa(2m), and xcex2, which is a root of said Gpb(x) and a primitive element of said GFb(2m), following Equation (25) is established; said RSb code is a t-symbol correction code, and its code forming polynomial Gcb(x) is represented by following Equation (26); when said input encoding target data is encoded by means of said RSb code, said first Galois field transformation means transforms said input encoding target data from said Galois field GFb(2m) into data of said Galois field GFa(2m); said encoding means performs encoding corresponding to following Equation (27), which is the polynomial transforming said code forming polynomial Gcb(x) into said Galois field GFa(2m); and said second Galois field transformation means inverse-transforms said encoded data from said Galois field GFa(2m) into data of said Galois field GFb(2m).                                           Gp            b                    ⁡                      (                          α              p                        )                          =        0                            Equation        ⁢                  xe2x80x83                ⁢        25                                                                    Gc              b                        ⁡                          (              x              )                                =                                    ∏                              j                =                0                            L                        ⁢                          xe2x80x83                        ⁢                          (                              x                +                                  β                                      q                    ⁡                                          (                                              b                        +                        j                                            )                                                                                  )                                      ,                  xe2x80x83                ⁢                  L          =                                    2              ⁢              t                        -            1                          ,                  xe2x80x83                ⁢                  or          ⁢                      xe2x80x83                    ⁢          2          ⁢          t                                    Equation        ⁢                  xe2x80x83                ⁢        26                                                                    Gc              ba                        ⁡                          (              x              )                                =                                    ∏                              j                =                0                            L                        ⁢                          xe2x80x83                        ⁢                          (                              x                +                                  α                                      pq                    ⁡                                          (                                              b                        +                        j                                            )                                                                                  )                                      ,                  xe2x80x83                ⁢                  L          =                                    2              ⁢              t                        -            1                          ,                  xe2x80x83                ⁢                  or          ⁢                      xe2x80x83                    ⁢          2          ⁢                      t            .                                              Equation        ⁢                  xe2x80x83                ⁢        27            
Also, the Reed-Solomon encoding device of the present invention is preferably characterized by the following features: for said first Galois field transformation means, when m of the 2m input/output relationships are represented by a transposed matrix ( . . . )T, with respect to m-bit input (00 . . . 0001)T, m-bit output A1=(00 . . . 001)T is performed; with respect to m-bit input (00 . . . 0010)T, m-bit output A1=(A1,mxe2x88x921, A1,mxe2x88x922, . . . A1,0)T is performed; with respect to m-bit input (00 . . . 0100)T, m-bit output A2=(A2,mxe2x88x921, A2,mxe2x88x922, . . . A2,0)T is performed; with respect to m-bit input (01 . . . 0000)T, m-bit output Amxe2x88x922=(Amxe2x88x922,mxe2x88x921, Amxe2x88x922,mxe2x88x922, . . . Amxe2x88x922,0)T is performed; with respect to m-bit input (10 . . . 0000)T, m-bit output Amxe2x88x921=(Amxe2x88x921,mxe2x88x921, Amxe2x88x921,mxe2x88x922, . . . Amxe2x88x921,0)T is performed; when mxc3x97m matrix [Hba] is defined by following Equation (28), with respect to said m-bit input data Db-in, arithmetic operation is performed according to following Equation (29) to form m-bit output data Da-out.                               [                      H            ba                    ]                =                  (                                    A                              m                -                1                                      ⁢                          A                              m                -                2                                      ⁢                          xe2x80x83                        ⁢            …            ⁢                          xe2x80x83                        ⁢                          A              2                        ⁢                          A              1                        ⁢                          A              0                                )                                    Equation        ⁢                  xe2x80x83                ⁢        28                                          D                      a            ⁢                          -                        ⁢            out                          =                              [                          H              ba                        ]                    xc3x97                                    D                              b                ⁢                                  -                                ⁢                in                                      .                                              Equation        ⁢                  xe2x80x83                ⁢        29            
Also, for the Reed-Solomon encoding device, it is preferred that said parameter output means outputs said matrix [Hba] as said first Galois field transformation parameter to said first Galois field transformation means.
Also, the Reed-Solomon encoding device of the present invention preferably has the following features: said parameter output means outputs rows of said matrix [Hba] as said first Galois field transformation parameter to the first Galois field transformation means in the order of rows; said first Galois field transformation means has the following means: multiple AND operation means corresponding in number to said bit data and performing the following operation: inputting from the first input terminal the bit data corresponding to the rows of said matrix [Hba] input as said first Galois field transformation parameter, inputting from the second input terminal the corresponding bit data of said input encoding target data, and performing a logical AND operation on said bit data input from the first input terminal and said bit data input from the second input terminal; and an exclusive-OR operation means that operates to get exclusive-OR of the operation results of said multiple AND operation means.
Also, for the Reed-Solomon encoding device of the present invention, it is preferred that when the inverse matrix of said matrix [Hba] is taken as [Hab], said second Galois field transformation means perform arithmetic operation according to following Equation (30) to form m-bit output data Db-out.                               D                      b            ⁢                          -                        ⁢            out                          =                              [                          H              ab                        ]                    xc3x97                      D                          a              ⁢                              -                            ⁢              in                                                          Equation        ⁢                  xe2x80x83                ⁢        30            
Also, for the Reed-Solomon encoding device of the present invention, it is preferred that said parameter output means output said matrix [Hab] as said second Galois field transformation parameter to said second Galois field transformation means.
Also, the Reed-Solomon encoding device preferably has the following features: said parameter output means outputs rows of said matrix [Hab] as said second Galois field transformation parameter to the second Galois field transformation means in the order of rows; said second Galois field transformation means has the following means: multiple AND operation means corresponding in number to said bit data and performing the following operation: input from the first inputting terminal the bit data corresponding to rows of said matrix [Hab] input as said second Galois field transformation parameter, inputting from the second input terminal the corresponding bit data of said encoded data, and performing a logical AND operation on said bit data input from the first input terminal and said bit data input from the second input terminal; and an exclusive-OR operation means that performs an exclusive-OR operation on the results of said multiple AND operations.
Also, it is preferred that the Reed-Solomon encoding device of the present invention also includes a multiplication coefficient memory means, and that said parameter output means sends the multiplication coefficients stored in said multiplication coefficient memory means to said multiplier.
Also, the present invention provides a type of Reed-Solomon decoding device characterized by the fact that the Reed-Solomon decoding device that corresponds to multiple RS codes by means of different field formation polynomials comprises the following means: a first Galois field transformation means that transforms the input decoding target data into prescribed Galois field data on the basis of the first input Galois field transformation parameters, a decoding means that performs the decoding process by means of said transformed Galois field for said transformed decoding target data, a second Galois field transformation means that inverse-transforms said decoded data into said Galois field data before transformation on the basis of the second input Galois field transformation parameters, and a parameter output means that outputs said first Galois field transformation parameter and said second Galois field transformation parameter.
In the Reed-Solomon decoding device of the present invention, a first Galois field transformation means and a second Galois field transformation means are arranged. For any of multiple RS codes, decoding processing is performed using a prescribed Galois field in the decoding means. As a result, there is no need to use multiplier and inverse element arithmetic unit to correspond to each of the multiple RS codes separately in the decoding means, so that the circuit scale can be reduced significantly.
Also, because said first Galois field transformation means and second Galois field transformation means perform Galois field transformation on the basis of the first Galois field transformation parameters and second Galois field transformation parameters output from the parameter output means, respectively, it is possible to make diverse and flexible changes for the contents of the Galois field transformation.
For the Reed-Solomon decoding device of the present invention, it is preferred that said decoding means have a multiplier corresponding to said transformed Galois field.
Also, the Reed-Solomon decoding device of the present invention preferably has the following features: said multiple RS codes are RSa codes and RSb codes using different field formation polynomials; the encoding symbols are Galois fields GFa(2m) and GFb(2m) extended on the basis of the different mth field formation polynomials Gpa(x) and GPb(x) on Galois field GF(2), respectively; with respect to xcex1, which is a root of said Gpa(x) and a primitive element of said GFa(2m), and xcex2, which is a root of said Gpb(x) and a primitive element of said GFb(2m), the following Equation (31) is established; said RSb code is a t-symbol correction code, and its code forming polynomial Gcb(x) is represented by following Equation (32); when said input decoding target data is decoded, said first Galois field transformation means transforms said decoding target data from said Galois field GFb(2m) into data of said Galois field GFa(2m); said decoding means performs decoding corresponding to the following Equation (33) that is the polynomial transforming said code forming polynomial Gcb(x) into said Galois field GFa(2m); and said second Galois field transformation means transforms said decoded data from said Galois field GFa(2m) into data of said Galois field GFb(2m).                                           Gp            b                    ⁡                      (                          α              p                        )                          =        0                            Equation        ⁢                  xe2x80x83                ⁢        31                                                                    Gc              b                        ⁡                          (              x              )                                =                                    ∏                              j                =                0                            L                        ⁢                          xe2x80x83                        ⁢                          (                              x                +                                  β                                      q                    ⁡                                          (                                              b                        +                        j                                            )                                                                                  )                                      ,                  xe2x80x83                ⁢                  L          =                                    2              ⁢              t                        -            1                          ,                  xe2x80x83                ⁢                  or          ⁢                      xe2x80x83                    ⁢          2          ⁢          t                                    Equation        ⁢                  xe2x80x83                ⁢        32                                                                    Gc              ba                        ⁡                          (              x              )                                =                                    ∏                              j                =                0                            L                        ⁢                          xe2x80x83                        ⁢                          (                              x                +                                  α                                      pq                    ⁡                                          (                                              b                        +                        j                                            )                                                                                  )                                      ,                  xe2x80x83                ⁢                  L          =                                    2              ⁢              t                        -            1                          ,                  xe2x80x83                ⁢                  or          ⁢                      xe2x80x83                    ⁢          2          ⁢          t                                    Equation        ⁢                  xe2x80x83                ⁢        33            
Also, the Reed-Solomon decoding device of the present invention preferably has the following features: for said first Galois field transformation means, when m of the 2m input/output relationships are represented by a transposed matrix ( . . . )T, with respect to m-bit input (00 . . . 0001)T, m-bit output A1=(00 . . . 001)T is performed; with respect to m-bit input (00 . . . 0010)T, m-bit output A1=(A1,mxe2x88x921, A1,mxe2x88x922, . . . A1,0)T is performed; with respect to m-bit input (00 . . . 0100)T, m-bit output A2=(A2,mxe2x88x921, A2,mxe2x88x922, . . . A2,0)T is performed; with respect to m-bit input (01 . . . 0000)T, m-bit output Amxe2x88x922=(Amxe2x88x922,mxe2x88x921, Amxe2x88x922,mxe2x88x922, . . . Am2,0)T is performed; with respect to m-bit input (10 . . . 0000)T, m-bit output Amxe2x88x921=(Amxe2x88x921,mxe2x88x921, Amxe2x88x921,mxe2x88x922, . . . Amxe2x88x921,0)T is performed; when mxc3x97m matrix [Hba] is defined by following Equation (34), with respect to said m-bit input data Db-in, arithmetic operation is performed according to following Equation (35) to form m-bit output data Da-out.                               [                      H            ba                    ]                =                  (                                    A                              m                -                1                                      ⁢                          A                              m                -                2                                      ⁢                          xe2x80x83                        ⁢            …            ⁢                          xe2x80x83                        ⁢                          A              2                        ⁢                          A              1                        ⁢                          A              0                                )                                    Equation        ⁢                  xe2x80x83                ⁢        34                                          D                      a            ⁢                          -                        ⁢            out                          =                              [                          H              ba                        ]                    xc3x97                      D                          b              ⁢                              -                            ⁢              in                                                          Equation        ⁢                  xe2x80x83                ⁢        35            
Also, for the Reed-Solomon decoding device of the present invention, it is preferred that said parameter output means outputs said matrix [Hba] as said first Galois field transformation parameters to said first Galois field transformation means.
Also, the Reed-Solomon decoding device of the present invention preferably has the following features: said parameter output means outputs rows of said matrix [Hba] as said first Galois field transformation parameter to the first Galois field transformation means in the row order; said first Galois field transformation means comprises the following means: multiple AND operation means corresponding in number to said bit data and performing the following operation: inputting from the first input terminal the bit data corresponding to the rows of said matrix [Hba] input as said first Galois field transformation parameter, inputting from the second input terminal the corresponding bit data of said input decoding target data, and performing a logical AND operation on said bit data input from the first input terminal and said bit data input from the second input terminal; and an exclusive-OR operation means that performs an exclusive-OR operation on the results of said multiple AND operations.
Also, for the Reed-Solomon decoding device of the present invention, it is preferred that when the inverse matrix of said matrix [Hba] is taken as [Hab], said second Galois field transformation means perform arithmetic operation according to following Equation (36) to form m-bit output data Db-out.                               D                      b            -            out                          =                              [                          H              ab                        ]                    xc3x97                      D                          a              -              in                                                          Equation        ⁢                  xe2x80x83                ⁢        6            
Also, for the Reed-Solomon decoding device of the present invention, it is preferred that said parameter output means output said matrix [Hab] as said second Galois field transformation parameter to said second Galois field transformation means.
Also, the Reed-Solomon decoding device of the present invention preferably has the following features: said parameter output means outputs rows of said matrix [Hab] as said second Galois field transformation parameter to the second Galois field transformation means in the order of rows; said second Galois field transformation means has the following means: multiple AND operation means corresponding in number to said bit data and performing the following operation: inputting from the first input terminal the bit data corresponding to the rows of said matrix [Hab] input as said second Galois field transformation parameter, inputting from the second input terminal the corresponding bit data of said encoded data, and performing a logical AND operation on said bit data input from the first input terminal and said bit data input from the second input terminal; and an exclusive-OR operation means that performs an exclusive-OR operation on the results of said multiple AND operations.
Also, it is preferred that the Reed-Solomon decoding device of the present invention also comprises a multiplication coefficient memory means, and that said parameter output means send the multiplication coefficients stored in said multiplication coefficient memory means to said multiplier.